Root Mean Square Ratio Research Articles

Frequency Distribution of the Normal Modes of Vibration in Rectangular Rooms

Several investigators, notably R. H. Bolt and D. Y. Maa, have examined the statistical distribution of the normal vibration frequencies in rectangular rooms. However, more definitive information would be useful, both for evaluating existing rooms and for optimizing the design of new acoustical laboratories, music rooms or recording studios. Among such information would be more detailed and precise knowledge of the effect of the relative room dimensions on the distribution of its normal modes. An IBM 7090 computer has been programed to determine the frequency distribution of the normal modes of rectangular rooms in each half octave interval over the range of the first four octaves. Frequency has been normalized with respect to the gravest mode, and dimension ratios will be varied from a cube to 5 to 1 parallelepipeds in steps as small as 1%. The principal criterion computed is the rms ratio between the actual mode spacing and the ideal spacing over each half-octave interval. The average mode spacing and, if needed, a more sensitive indicator to help determine the “best” room dimension ratio also will be computed. This paper discusses the equations used, the criteria to be computed, and the results obtained to date.